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Mind Games
Posted Mar 24,2009


Lawrence Weinstein doesn’t know how many jelly beans are in this jar, but he has a very good guess. And it’s higher than you might expect. Weinstein, who teaches estimation at Virginia’s Old Dominion University, has a knack for solving problems with little data. His secret is more method than magic: Break questions into pieces, approximate, and use metric units for easier math.

Fermi estimation, as such a method is known, helps experts decide if problems— from jelly bean counts to carbon counts—warrant further calculation. Precision isn’t always necessary. Take sea level rise. By assuming the thickness of the Antarctic ice sheet (1,000 meters) and dividing that by how many Antarcticas he thought would cover the Earth (30), Weinstein surmised that melting ice caps could raise sea levels at least 30 meters. Though USGS reports suggest a 73-meter rise (80 meters if you include Greenland’s ice sheet), his rough guess still predicts catastrophe. “I don’t need to refine that number,” says Weinstein. “I’m in Virginia Beach. Either way, I’m underwater.” —Oliver Uberti

ANYONE’S GUESS You don’t have to split atoms to guess how many jelly beans are in this jar. Simply break the problem into steps.

1 Approximate the jar’s radius (r) in beans. (Hint: Count the jar's width, then divide by two.)
2 Estimate its height (h) in beans.
3 Use these numbers to figure the jar’s occupied volume: V = πr2 x h. Round π off to three.
4 Gloat (Put your mouse over the jar photo and wait for the answer.)

Photo: Mark Thiessen, NG Photographer

Posted by National Geographic Staff | Comments (5)
Filed Under: Science, Wide Angle
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Richard Weih
Mar 24, 2009 5PM #

What numbers were used to get the answer. I tried it and came up with a much larger number using the given formula.

Oliver Uberti
Mar 24, 2009 5PM #

Richard, I hand-counted all 4,466 jelly beans. It took over two hours on a sad Thursday night. But before I did that, I followed Weinstein's estimation formula. I used a radius of 7 and a height of 30. So in V = (pi)r^2 * h, I figured a volume of (3)(7*7) * 30 = roughly 4500. A difference of only 34 beans!

In Fermi estimation, scientists are not looking for precision; they just want to be in the ballpark. Says John A. Adam, professor of mathematics at Old Dominion University, "if the “method” gives a correct answer to within a factor of two, that’s pretty good."

**Remember to count the jar's radius (half the width) instead of its diameter.

C. J. Oakley
Mar 24, 2009 5PM #


Nice work!

Mar 24, 2009 5PM #

I was excited to see this in our magazine. I just finished my Science Fair experiment and I had boys and girls guess how many jellybeans were in the jar.

My hypothesis was girls would be better than boys but I was wrong. Both genders tended to underestimate.

Total: 1576. I wish I had 4000+!

I am saving this and putting it in my notebook.


Buy WoW Mage
Mar 24, 2009 5PM #

Thank you for posting the mind games. I've been playing different online games and so far I find it very much interesting to play. Keep it up and please keep posting!

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